Since the financial crisis, hedge funds for the most part have struggled to produce strong returns relative to passive strategies, making it difficult to justify the fees they're paid.

Typically, fund managers are paid through a compensation structure commonly known as the "2 and 20," which stands for a 2% management fee and a 20% performance fee. More specifically, "2 and 20" means a hedge fund manager would charge investors 2% of total assets under management and 20% of any profits. The fees can vary from fund to fund, with some charging less and others charging more such as "3 and 30."

In Singer's latest investor letter, dated Jan. 30, he writes that investment banks "are effectively big, highly leveraged hedge funds." He said his team conducted some analysis to see how banks compared with hedge funds in terms of compensation and costs. Singer writes that banker compensation "as a percentage of value produced at major banks is significantly higher than at hedge funds.

"At the very least, it calls into question the rationale of investors who comfortably own significant positions in major financial institutions but confine their criticisms of complexity and compensation to hedge funds."

Here's the excerpt from Singer's letter:

In our last quarterly report, we took a swipe at CALPERS' decision to exit hedge funds. After sending out the report, we had a minor epiphany. We have been (correctly) saying that the world's major financial institutions are effectively the largest hedge funds on the planet, with their fortunes dominated by trading results, however packaged. At the same time, some institutional investors are cranky that the returns of hedge funds during the six years (and counting) since the introduction of QE have been less than unhedged stock and bond returns during that period, and that hedge funds are too complicated and their fees and costs too high. These investors may have forgotten that before the financial crisis, many carefully selected hedge funds performed admirably in controlling risk and generating a true diversity of returns. This combination got us thinking: Since the financial institutions are effectively big, highly-leveraged hedge funds, we wondered how they compared with hedge funds in terms of compensation and costs.

The results of our team's study of this comparison (don't worry, it didn't take much time) were quite enlightening. Using reported market and financial performance for 2014, we found the bottom line is clear: By every measure, employee compensation at major financial institutions is significantly higher than that at hedge funds.

We surveyed the five major U.S.-based investment banks and found that employee compensation accounted for 59% of the "gross adjusted change in market capitalization" — the increase in market capitalization in addition to buybacks and dividends, and after adding back compensation expense. It was 64% of "gross adjusted pretax income" — GAAP pretax income after adding back compensation expense. At hedge funds, employee compensation accounted for 23% of "gross adjusted returns" — net returns with compensation expense added back. Similar results were obtained when examining employee expenses as a percentage of capital. Bank compensation was 19% and 22% of beginning market capitalization and tangible book value, respectively, compared with 3.1% of total capital for hedge funds.

Although undoubtedly there are certain nuances and distinctions, we believe our analytical approach, if anything, is likely to be more, not less, generous to large financial institutions. For instance, the adjusted change in market value benefits from a year in which bank multiples generally expanded. Nor did we subtract from bank earnings the value of the considerable subsidy these institutions enjoy from their "too big to fail" status. Nevertheless, and keeping these considerations in mind, we think these analyses are meaningful in demonstrating that employee compensation as a percentage of value produced at major banks is significantly higher than at hedge funds. At the very least, it calls into question the rationale of investors who comfortably own significant positions in major financial institutions but confine their criticisms of complexity and compensation to hedge funds.

Singer, who has an estimated net worth of $1.86 billion, is also ranked No. 9 for the all-time performing hedge fund managers, according to fund-of-funds LCH Investments.

In 2014, Elliott returned 8.2% compared to the S&P 500's 13% rise. Hedge funds, on average, returned only 3.78% last year, according to the research firm Preqin.